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*"velocity is the same before and after the collision"*the velocity can be determined by dividing the initial velocity by the ratio of m

_{new}:m

_{old}. In other words, mass and velocity are inversely proportional:

http://www.physicsclassroom.com/class/momentum/Lesson-2/Using-Equations-as-a-Guide-to-Thinking

(This is the animation): http://www.physicsclassroom.com/mmedia/momentum/fca.cfm

But then, how is velocity the same before and after if it's obviously changing? And when would this situation of being able to find the new velocity by a simple ratio

__not work__?

Thanks, and I know this is going to be a very simple answer pointing out something I missed, but I'm just stumped :D.